Well I say easy, but it's not that easy. Total time was around eight hours including server firmware updates.

  1. Upgrade vCenter Server (I used the appliance, so download the appropriate files from the VMware site) - this is done by booting both, new one has DHCP, copying keys in the web interface so they can speak to each other and finally restarting and deleting the old server. Make sure you update the original server through the web interface before continuing! I wasted a good two hours waiting on it upgrading  but it never did so I had to start again.
  2. Check you can connect and see all the hosts, and that everything works OK.
  3. Shut down all VMs and hosts.
  4. I used the easier (in my opinion) option of using iLO to upgrade ESXi, I connected through IE so I could mount the virtual disk (ESXi 5.1 HP specific ISO file) and install. This works great for Essentials or Essentials Plus customers - Enterprise customers should use the Update Manager.
  5. Boot into the installer and make sure you choose the upgrade option, when it asks which disk to choose use the one without an asterisk (this is local storage, may be different for SAN) - the one(s) with asterisk(s) are your VMFS partitions containing VM files.
  6. Reboot each host, check you can connect to the host, boot your vCenter, make sure you can connect to it and it should see all hosts and be working fine! You may need to update your backup software to account for having a new version of ESXi on the hosts.